# Important Questions Class 7 Maths Chapter 12

## Important Questions Class 7 Mathematics Chapter 12 – Algebraic Expressions

Mathematics is a major subject you study in school. You know that we need Mathematics in every aspect of our lives. From calculating everyday expenses to large-scale construction, Mathematics helps us every time.

Chapter 12 is about algebraic expressions. Students will learn about the basics of algebra. It is an important branch of Mathematics, and students will use algebra more in higher classes. In previous chapters, they learned about variables and constants. In this chapter, they will learn how to construct an equation, do addition or subtraction, etc. They must practise questions as much as possible to score better in exams.

Extramarks is a leading company that provides all the important study materials. Our experts have made the Important Questions Class 7 Mathematics Chapter 12 to help students. They have collected the questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, NCERT Exemplars, and important reference books. They have also solved the questions, and experienced professionals have further checked the answers to ensure the best quality of the content.

Extramarks is one of the leading companies in India that provides all the important study materials. You can download the study materials after registering on our official website. We provide CBSE syllabus, CBSE sample papers, CBSE past years’ question papers, CBSE revision notes, CBSE extra questions, NCERT books, NCERT exemplars, NCERT solutions, NCERT important questions, important formulas, and many more.

### Important Questions Class 7 Mathematics Chapter 12 – With Solutions

Extramarks’ experts understand the needs of students. They have collated the questions from different sources, such as the textbook exercise, the CBSE syllabus, CBSE sample papers, CBSE past years’ question papers, and important reference books. They have also solved the questions so that students can follow the answers if they cannot solve the questions. Experienced professionals have further checked the solutions to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 12 will help students score better in exams. The important questions are-

Question 1. Using variables, constants and arithmetic operations, give the algebraic expression in the following cases.

• Give the algebraic expression for the subtraction of z from y.
• Give an algebraic expression of one-half of the sum of numbers x and y.
• Give an algebraic expression of the number z multiplied by itself.
• Give an algebraic expression of one-fourth of the product of numbers p and q.
• Give an algebraic expression of numbers x and y which are the numbers and both squared and added.
• Give the algebraic expression for number 5 added to three times the product of numbers m and n.
• Give the algebraic expression for products of numbers y and z subtracted from 10.
1. Give an algebraic expression of the sum of numbers a and b subtracted from their product.

Answer 1: The solution for the above options is given below:

1. Y – z
2. ½ (x + y)= (x+y)/2
3. z × z = z2
4. ¼ (p × q) = pq/4
5. X2 + y2
6. 3mn + 5
7. 10 – (y × z) = 10-yz
8. ( a × b) – ( a + b)= ab – (a + b)a

Question 2. Identify in the following expressions the terms and their factors.

• x – 3
• 1 + x + x2
• y – y3
• 5xy2 + 7x2y
• -ab + 2b2 – 3a2
• -4x + 5
• -4x + 5y
• 5y + 3y2
• xy + 2x2y2
• pq + q
• 1.2 ab – 2.4 b + 3.6 a
• ¾ X + ¼
• 0.1 p2 + 0.2 q2
 Expression Terms Factors x – 3 x, -3 x, -3 1 + x + x2 1, x, x2 1; x ; x, x y – y3 y, -y3 y; -y, -y, -y 5xy2 + 7x2y 5xy2, 7x2y 5, x, y, y; 7, x, x, y -ab + 2b2 – 3a2 -ab, 2b2, – 3a2 -a, b; 2, b, b; -3, a, a -4x + 5 -4x, 5 -4, x, 5 -4x + 5y -4x, 5y -4, x ; 5, y 5y + 3y2 5y, 3y2 5, y; 3, y, y xy + 2x2y2 xy, 2x2y2 x, y, ; 2, x, x, y, y pq + q pq, q p, q, q 1.2 ab – 2.4 b + 3.6 a 1.2 ab, 2.4 b, 3.6 a 1.2, a, b, 2.4, b, 3.6, a ¾ X + 1/4 ¾ X, ¼ ¾, X, ¼ 0.1 p2 + 0.2 q2 0.1 p2 , 0.2 q2 0.1, p, p, 0.2, q, q

Question 3. What is an expression, and a coefficient. Identify the numerical coefficient of terms other than constants in the following expressions.

• 5 – 3t2
• 1 + t + t2 + t3
• x + 2xy + 3y
• 100m + 100n
• -p2q2 + 7pq
• 1.2 a + 0.8 b
• 3.14 r2
• 2 ( I + b)
• 0.1 y + 0.01 y2

An algebraic expression is the combination of variables and constants which are connected by the signs of fundamental operations means +, – , ×, ÷

Some of the examples of algebraic expression are:

2x + 3y

5 m × n -2q

5a ÷ b + 3c

Coefficient is defined as the number multiplied by a variable or variables.

In 3x, the coefficient is 3

In 5yz, coefficient is 5

 Expression Terms Coefficients 5 – 3t2 – 3t2 -3 1 + t + t2 + t3 t  t2  t3 1 1 1 x + 2xy + 3y x, 2xy ,3y 1, 2, 3 100m + 1000n 100m, 1000n 100, 1000 -p2q2 + 7pq -p2q2 , 7pq -1, 7 1.2 a + 0.8 b 1.2 a , 0.8 b 1.2, 0.8 3.14 r2 3.14 r2 3.14 2 ( I + b) 2I, 2b 2, 2 0.1 y + 0.01 y2 0.1 y, 0.01 y2 0.1, 0.01

Question 4. Identify the terms which contain x ( 1 to 7 )or y (8 to 10) separately  and give the coefficient for x or y in the table form.

• y2x + y
• 13 y2 – 8yx
• x + y + 2
• 5 + z + zx
• 1 + x + xy
• 12 xy2 + 25
• 7x + xy2
• 8 – xy2
• 5y2 + 7x
• 2x2y – 15xy2 + 7y2

 Expression Terms Coefficient of x y2x + y y2x y2 13 y2 – 8yx -8yx -8y x + y + 2 x 1 5 + z + zx x, zx 1, z 1 + x + xy xy y 12 xy2 + 25 12 xy2 12 y2 7x + xy2 7x, xy2 7, y2 Expression Term Coefficient of y2 8 – xy2 -xy2 -x 5y2 + 7x 5y2 5 2x2y – 15xy2 + 7y2 -15xy2, 7y2 -15x, 7

Question 5. Identify the like terms in the following:

• -xy2, 3x, 2xy, -4yx2, y,8x2, 2xy2, -6x2, 20x2y, -11yx, -11×2, -100x, 2xy2, 7y
• 10pq, 100q, 701p2, qp2,13p2q,7p, 8q, -7qp, -p2q2, -23, 12q2p2, -5p2, 41, 2405p, 78qp

Answer 5: In the questioned mentioned above, when term have the same algebraic factors, they are like terms. Based on this, the like term can be written as:

1. -xy2, 2xy2

-4yx2, 20x2y

8x2, -11x2, -6x2

7y, y

-100x, 3x

-11yx, 2xy

1. 10pq, -7qp, 78qp

7p, 2405p

8q, -100q

-p2q2, 12q2p2

-23, 41

-5p2, 701p2

13p2q, qp2

Question 6. The pairs are given below, choose like and unlike terms from them and mention reason.

• 1, 100
• -7 x , 5/2 x
• -29 x, -29 y
• 14 xy, 42 yx
• 4 m2p, 4 mp2
• 12 xz, 12 x2z2

1. This is the pair of like terms because they have the same algebraic factors.
2. This is the pair of like terms because they have the same algebraic factors.
3. This is the pair of unlike terms because the algebraic factors are different.
4. This is the pair of like terms because they have the same algebraic factors.
5. This is the pair of unlike terms because the algebraic factors are different.
6. This is the pair of unlike terms because the algebraic factors are different.

Question 7. What are monomials, binomials, and trinomials. Classify the following into these with reason.

• 4y – 7z
• y2
• x + y – xy
• 100
• Ab – a – b
• 5 – 3t
• 4p2q – 4pq2
• 7mn
• z2 – 3z + 8
• A2 + b2
• Z2 + z
• 1 + x + x2

An expression which contains only one term is known as a monomial. When two terms are present in an expression it is called binomial. A Trinomial is when the expression contains three terms.

If a trinomial is a perfect square, then it is the square of a binomial.

 Question Category Reason 4y – 7z Binomial Two unlike terms y2 Monomial Only one term x + y – xy Trinomial Has three terms 100 Monomial One term ab – a – b Trinomial Three term 5 – 3t Binomial Has two unlike terms 4p2q – 4pq2 Binomial Has two unlike terms 7mn Monomial Has only one term z2 – 3z + 8 Trinomial Has three terms a2 + b2 Binomial Has two unlike terms z2 + z Binomial Has two unlike terms 1 + x + x2 Trinomial Has three terms

Question 8. Fill in the blanks:

• An algebraic expression in which the variables involved have only non-negative integer powers

is called a __________.

• Terms having the same literal coefficients are called __________.
• _____________are those terms having different literal coefficients.
• Every polynomial is an _________, but every expression need not be a ________
• The polynomial degree is the highest degree of a _________which is present in the

polynomial.

• The number for which the value of a polynomial is zero is called ____________.
•  If a trinomial is a perfect square, then it is the square of a __________.
• The parts of an algebraic expression are separated by the __________.
• _________ is the number multiplied by a variable or variables.
• If the sum of the coefficient is zero then the whole term becomes ________
• __________ in mathematics are written in a concise manner.
• The value of expression depends on the value of _________
• Algebraic expressions are formed from _______ and _______
• The operations used on the variables are _____, ______, _______ and _______
• Expressions are made up of _______
• A term is a ________
• The numerical factor in the term is called the ________
• Terms add and make ________

1. An algebraic expression in which the variables involved have only non-negative integer powers

is called a polynomial.

1. Terms having the same literal coefficients are called like terms.
2. Unlike terms are those terms having different literal coefficients.
3. Every polynomial is an expression, but every expression need not be a polynomial.
4. The polynomial degree is the highest degree of a monomial which is present in the

polynomial.

1. The number for which the value of a polynomial is zero is called zero of the polynomial.
2.  If a trinomial is a perfect square, then it is the square of a binomial.
3. The parts of an algebraic expression are separated by the operational.
4. Co-efficient  is the number multiplied by a variable or variables.
5. If the sum of the coefficients is zero then the whole term becomes zero
6. Algebraic expressions in mathematics are written in a concise manner.
7. The value of the expression depends on the value of the variables.
8. Algebraic expressions are formed from variables and constants.
9. The operations used on the variables are addition, subtraction, multiplication and division.
10. Expressions are made up of terms
11. A term is a product of factors
12. The numerical factor in the term is called the coefficient
13. Terms add and make expressions.

Question 9. Simplify combining the terms given below:

• 21b – 32 + 7b – 20b
• a– (a – b) – b – (b – a)
• 3a – 2b – ab- (a – b + ab) + 3ab + b – a

Solution:

1. They are like terms as they have the same algebraic factors. So it can be presented as

= (21b + 7b – 20b) – 32

=b (21 + 7 – 20) – 32

= b (28 – 20) – 32

= b (8) – 32

= 8b – 32

1. These are like terms as the terms have the same algebraic factors. So it could be presented as:

= a – a + b – b – b + a

= a – b

1. When the terms have the same algebraic factors then they are like terms. So it could be presented as:

= 3a – 2b – ab – a + b – ab + 3ab + b – a

= 3a – a – a – 2b + b + b – ab – ab + 3ab

= a (1 – 1 – 1) + b (-2 + 1 + 1) + ab ( -1 -1 + 3)

= a(1 – 2) + b ( -2 + 2) + ab ( -2 + 3)= a(1) + b (0) + ab(1) = a + ab

Question 10. Add the following given below:

• 3mn, -5mn, 8mn, -4mn
• t – 8tz, 3tz – z, z – t
• -7mn + 5, 12mn + 2, 9mn – 8, -2mn-3
• a + b – 3, b – a + 3, a – b + 3

1. In the given question, all are the like terms as they have the same algebraic factors so when the like terms are added, it could be presented as:

3mn + (-5mn) + 8mn + (-4mn) = 3mn – 5mn + 8mn – 4mn

=mn ( 3 – 5 + 8 – 4)

=mn (11 – 9)

=mn (2) = 2mn

1. In the given question, all are the like terms as they have the same algebraic factors so when the like terms are added, it could be presented as:

= t – 8tz + (3tz – z) + (z – t)

= t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

=t (1 -1) + tz (-8 + 3) + z (-1 + 1)

=t (0) + tz (-5) + z (0)

=-5 tz

1. In the given question, all are the like terms as they have the same algebraic factors so when the like terms are added, it could be presented as:

= -7mn + 5 + 12mn + 2 + (9mn – 8) + ( -2mn – 3)

= -7mn + 5 + 12mn + 2 + 9mn – 8 – 2mn – 3

= -7mn + 12mn + 9mn – 2mn + 5+ 2 – 8 – 3

=mn (-7 + 12 + 9 – 2) + ( 5 + 2 – 8 – 3)

=mn ( -9 + 21) + (7 – 11)

= mn (12) – 4

= 12mn – 4

1. In the given question, all are the like terms as they have the same algebraic factors so when the like terms are added, it could be presented as:

= a + b – 3 + (b – a + 3) + (a – b + 3)

=a + b – 3 + b – a + 3 + a – b + 3

= a – a + a + b + b – b -3 + 3 + 3

= a(1 -1 + 1) + b(1 + 1 – 1) + (-3 + 3 + 3)

=a (2 -1 ) + b ( 2 -1 ) + (-3 + 6)

= a (1) + b (1) + (3)

= a + b + 3

Question 11. Write an expression for a number 8 which is subtracted from the sum of x and 3.

Answer 11: As per the given statement the equation will be written as:

(x + 3 ) – 8

Question 12. Simplify the following equation:

3 ( 2x + 1) + 4x + 15 when the given value of x is -1.

We are given the equation as,

3 ( 2x + 1) + 4x + 15

This is the quadratic equation

on substituting the value of x as -1, we get

= 3 [2 (-1) + 1] + 4(-1) + 15

= 3(-2 + 1 ) – 4 + 15

= – 3 – 4 + 15

= – 7 + 15

= 8

Question 13. What is the value of the equation given that x = 8?

3x2 – 4x + 8

Answer 13: The given equation is,

3x2 – 4x + 8

= 3(8)2 – 4(8) + 8

= 3 (64) – 32 + 8

= 192 – 32 + 8

= 168

Question 14. When m = 0 ,calculate the value of p, The equation given is

3 m2 + m + p = 12

Solution 14.

3 m2 + m + p = 12

3 (0) + 0 + p = 12

p = 12

As calculated the value of p is 12

Question 15. Subtract the given below:

(i) –4x2 from x2

Solution:-

The term given has the same algebraic factors, so they are like terms.

On subtraction of these like terms, we will get

= x2 – (-4x2)

= x2 + 4x2

= 5x2

(ii) 6ab from –11ab

Solution:-

The term given has the same algebraic factors, so they are like terms.

On subtraction of these like terms we will get

= -11ab – 6ab

= – 17ab

(iii) (x– y) from (x + y)

Solution:-

The term given has the same algebraic factors, so they are like terms.

On subtraction of these like terms we will get

= (x + y) – (x – y)

= x + y – x + y

= x – x + y + y

= x (1 – 1) + y (1 + 1)

= x (0) + y (2)

= 2y

(iv) x (y – 5) from y (5 – x)

Solution:-

The term given has the same algebraic factors, so they are like terms.

On subtraction of these like terms we will get

= y (5 -x) – x (y – 5)

= 5y – xy – xy + 5x

= 5y + xy (-1 -1) + 5x

= 5x + 5y – 2xy

(v) –x2 + 5xy from 4x2 – 3xy + 8

Solution:-

The term given has the same algebraic factors, so they are like terms.

On subtraction of these like terms we will get

= 4x2 – 3xy + 8 – (- x2 + 5xy)

= 4x2 – 3xy + 8 + x2 – 5xy

= 4x2 + x2 – 3xy – 5xy + 8

= 5x2 – 8xy + 8

(vi) – a2 + 10a – 5 from 5a – 10

Solution:-

On subtraction, we will get

= 5a – 10 – (-a2 + 10x – 5)

= 5a – 10 + a2 – 10a + 5

= a2 + 5a – 10a – 10 + 5

= a2 – 5a – 5

Question 16.  From the sum of 4 + 3a and 5 – 4a + 2a2, subtract the sum of 3a2 – 5a and

–a2 + 2a + 5.

Solution:-

First we have to find out the sum of 4 + 3a and 5 – 4a + 2a2

= 4 + 3a + (5 – 4a + 2a2)

= 4 + 3a + 5 – 4a + 2a2

= 4 + 5 + 3a – 4a + 2a2

= 9 – a + 2a2

= 2a2 – a + 9 … This is the equation 1

To calculate the sum of 3a2 – 5a and –a2 + 2a + 5.

= 3 a2– 5a + (a2– + 2a + 5)

= 3a2 – 5a – a2 + 2a + 5

On rearranging,

= 3 a2– a2 – 5a + 2a + 5

= 2 a2– 3a + 5 —– this is the equation no 2

Now on subtraction of equation 2 from 1

= 2 a2– a + 9 – (2a2 – 3a + 5)

= 2a2 – a + 9 – 2 a2+ 3a – 5

= 2 a2– 2a2 – a + 3a + 9 – 5

= 2a + 4

### Benefits of Solving Important Questions Class 7 Mathematics Chapter 12

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## FAQs (Frequently Asked Questions)

### 1. What are the main concepts of Class 7 Mathematics Chapter 12?

In this chapter, students will learn about algebra, which is a big part of mathematics. The chapter is about algebraic equations and how to construct equations. The students will learn about variables and constants, addition and subtraction in equations, etc. Thus, students will learn about the basics of algebra. They must seek assistance from other sources to answer as many questions as possible.They can take help from the Important Questions Class 7 Mathematics Chapter 12 prepared by the experts at Extramarks.

### 2. How can the Important Questions Class 7 Mathematics Chapter 12 help students?

The textbook exercises are not enough for students. They must ask more questions to strengthen their concepts. The experts have made this question series to help students score better on exams. They have collected the questions from the textbook exercise, CBSE sample papers, CBSE past years’ question papers, and NCERT exemplars. They have also taken help from important reference books. Apart from this, they have solved each question, and experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 12 help students clarify their doubts, boost their confidence, and improve their exam marks.